A diving board is 12 feet above the ground. The bottom of the pool is 16 feet below the ground. Write and solve an equation that gives the distance from the diving board to the bottom of the pool.

Answer:

[tex] \displaystyle D) {x}^{5} + \rm C[/tex]

Step-by-step explanation:

we would like to integrate the following Integral:

[tex] \displaystyle \int 5 {x}^{4} \, dx [/tex]

well, to get the constant we can consider the following Integration rule:

[tex] \displaystyle \int c{x} ^{n} \, dx = c\int {x}^{n} \, dx[/tex]

therefore,

[tex] \displaystyle 5\int {x}^{4} \, dx [/tex]

recall exponent integration rule:

[tex] \displaystyle \int {x} ^{n} \, dx = \frac{ {x}^{n + 1} }{n + 1} [/tex]

so let,

Thus integrate:

[tex] \displaystyle = 5\left( \frac{ {x}^{4+ 1} }{4 + 1} \right)[/tex]

simplify addition:

[tex] \displaystyle = 5\left( \frac{ {x}^{5} }{5} \right)[/tex]

reduce fraction:

[tex] \displaystyle = {x}^{5} [/tex]

finally we of course have to add the constant of integration:

[tex] \displaystyle \boxed{ {x}^{5} + \rm C}[/tex]

hence,

our answer is D)

Answer:

A.  3 (1,2,3,4,5) B 60%

Step-by-step explanation:

Answer:

a) {1H,2H,3H,4H,5H,1T,2T,3T,4T,5T} b) 1H,3H,5H,1T,3T,5T

Step-by-step explanation:

a)

sample space is basically all possible outcomes in a list so {1H,2H,3H,4H,5H,1T,2T,3T,4T,5T}

b)

favorable outcomes of choosing an odd number are the outcomes with odd numbers so 1H,3H,5H,1T,3T,5T

[tex]\sf \: The \: formula \: for \: finding \: the \: volume \: of \: a \: cube \: is \hookrightarrow \boxed{ \underline{ \bf{E}^{3} }} \\ \\ \sf \: The \: volume \: of \: the \: cube \: can \: be \: found \: by \: \\ \sf \: multiplying \: the \: edge \: length \: three \: times. \: For \: instance, \: \\ \sf \: if \: the \: length \: of \: an \: edge \: of \: a \: cube \: is \: \bf \: 4, \: \sf t he \: volume \\ \sf \: will \: be \longrightarrow \bf{4}^{3}. [/tex]

Answer:

2

Step-by-step explanation:

Answer:

x = 1.4 or -1.4

Step-by-step explanation:

→ Substitute y = 4 into y = x² + 2

4 = x² + 2

→ Minus 2 from both sides

2 = x²

→ Square root both sides

√2 = x

→ Simplify

x = 1.4 or -1.4

Answer: um

Step-by-step explanation:

Answer:

y = -2x+7

Step-by-step explanation:

The slope intercept form of an equation is

y = mx+b  where m is the slope and b is the y intercept

y = -2x +b

Substitute the point into the equation and solve for b

5 = -2(1)+b

5 = -2+b

Add 2 to each side

5+2 = -2+b+2

7=b

y = -2x+7

Answer:

48 Chocolates

Step-by-step explanation:

Monday: 48

Tuesday: 24

Wednesday: 12

Thursday: 6

Friday: 3

Answer: $4.5/hour

Step-by-step explanation:

Total earned in 6 hours subtracted tips equals wage over 6 hours.

Divide by 6 hours to find individual hourly wage.

Answer: $4.50 per hour

Step-by-step explanation:

First, find how much she earned, excluding the tips.

73-46= 27

She earned $27 in the 6 hours, without tips

To find her hourly wage, you divide 27 by six because, since she worked 6 hours to earn $27, we need to find the unit rate.

27/6 = 4 dollars 50 cents.

Answer:

g = -1/2

Step-by-step explanation:

-10(g - 6) = 65

Distribute

-10g +60 = 65

Subtract 60 from each side

-10g+60-60 = 65-60

-10g = 5

Divide by -10

-10g/-10 = 5/-10

g = -1/2

[tex]\huge\text{Hey there!}[/tex]

[tex]\large\textsf{-10(g - 6) = 65}\\\\\rightarrow\large\textsf{-10g + 60 = 65}\\\\\large\text{SUBTRACT 60 to BOTH SIDES}\\\\\large\textsf{-10g + 60 - 60 = 65 - 60}\\\\\large\text{CANCEL out: 60 - 60 because that gives you 0}\\\\\large\text{KEEP: 65 - 60 because that helps you solve for your g-value}\\\\\large\textsf{65 - 60 = \bf 5}\\\\\large\text{DIVIDE -10 to BOTH SIDES}\\\\\mathsf{\dfrac{-10g}{-10}=\dfrac{5}{-10}}\\\\\large\text{CANCEL out:: }\mathsf{\dfrac{-10}{-10}}\large\text{ because that gives you 1}[/tex]

[tex]\large\text{KEEP: }\mathsf{\dfrac{5}{-10}}\large\text{ because that gives you the g-value answer}\\\\\large\textsf{g = }\mathsf{\dfrac{5}{-10}}\\\\\large\textsf{g =}\mathsf{\dfrac{5\div5}{-10\div5}}\\\\\large\textsf{g = }\mathsf{\bf - \dfrac{1}{2}}\\\\\\\\\boxed{\boxed{\large\textsf{Therefore, your answer is: g = }\mathsf{- \bf \dfrac{1}{2}}}}\huge\checkmark[/tex]

[tex]\huge\text{Good luck on your assignment \& enjoy your day!}\\\\\\\\\\\frak{Amphitrite1040:)}[/tex]

Answer:

Choice A. [tex]\frac{2}{3}[/tex]

Step-by-step explanation:

Turn the mixed numbers into improper fractions:

Flip the second term and multiply:

Simplify:

Answer:

A

Step-by-step explanation:

Answer:

150 = x

Step-by-step explanation:

We can use a ratio to solve

100 batches          x batches

------------------- = ---------------------

8 hours                12 hours

Using cross products

100 * 12 = 8x

1200 = 8x

Divide by 8

1200/8 = 8x/8

150 = x

Answer:

150

Step-by-step explanation:

Find how many batches in one hour

100/8 = 12.5

Multiply 12 hours with 12.5 batches

12 x 12.5 = 150

So, in 12 hours 150 batches are made.

Answer:

61.973

Step-by-step explanation:

let the unknow side be x

surf of prism = 2*(8*8+8x+8x) = 2*(64+16x) = 128+ 32x

again, surface of cylinder = 2pi*r*(r+h) = 2 * pi * 14 * (14+10) = 672pi

now solve for x, when

128+32x = 672pi

Answer:

i would say 7

Step-by-step explanation:

Answer

around 10%

Step-by-step explanation:

Step-by-step explanation:

Above are the explanations

A map is drawn on a scale of 1: 240 000.

(i) Actual area [tex]$=21.888 \mathrm{~km}^{2}$[/tex]

(ii) Area on the map = [tex]$0.505 \mathrm{~cm}^{2}$[/tex].

(i) 1 cm: 240000 cm = 1 cm: 2.4km

Area scale [tex]$=1^{2} \mathrm{~cm}^{2}: 2.4^{2} \mathrm{~km}^{2}$[/tex]

[tex]$=1 \mathrm{cm}^{2}: 5.76 \mathrm{~km}^{2}$[/tex]

[tex]$1 \mathrm{~cm}^{2}: 5.76 \mathrm{~km}^{2}$[/tex]

[tex]$3.8 \mathrm{~cm}^{2}: 21.888 \mathrm{~km}^{2}$[/tex]

Actual area [tex]$=21.888 \mathrm{~km}^{2}$[/tex]

[tex]$=21.9 \mathrm{~km}^{2}[/tex]

(ii) 1 cm: 240000 cm = 1 cm: 2400 m

Area scale [tex]$=1^{2} \mathrm{~cm}^{2}: 2400^{2} \mathrm{~m}^{2}$[/tex]

[tex]$=1 \mathrm{~cm}^{2}: 5760000 \mathrm{~m}^{2}$[/tex]

[tex]$1cm}^{2}: 5760000 \mathrm{~m}^{2}$[/tex]

[tex]$0.505 \mathrm{~cm}^{2} ; 2108800 \mathrm{~m}^{2}$[/tex]

The area on the map = [tex]$0.505 \mathrm{~cm}^{2}$[/tex].

To learn more about the area on the map

https://brainly.com/question/24103758

#SPJ2

Step-by-step explanation:

If we count for both numbers up to 36, we start seeing a pattern...

Candy: 6 12 18 24 30 36

Danny: 4 8 12 16 20 24 28 32 36

Every other number in Candy's counting is also counted by Danny. So here's what we'll do:

600/6 = 100

This is how many numbers Candy counted overall.

100/2 = 50

This is how many numbers Danny counted that were also numbers Candy counted.

Answer:

50 of the numbers that candy counted were also counted by Danny.

Answer:

50

Step-by-step explanation:

x = -29/7

Step-by-step explanation:

A(x) = (x^2 + 5x + 6)(x + 5) - (x^2 + 3x - 4)(x + 7)

= (x^3 + 10x^2 + 31x + 30) - (x^3 + 10x^2 + 17x - 28) = 14x + 58

A(x) = 0 => 14x + 58 =0 => x = -58/14 = -29/7

Answer:

778744

Step-by-step explanation:

387t98878989890

Answer:

[tex]y = x-7[/tex]

Step-by-step explanation:

Step 1:  Write the equation in point-slope form

Point Slope Form:  [tex]y-y_{1}=m\left(x-x_{1}\right)[/tex]

Plug in the numbers and solve

[tex]y - (-2) = 1(x - 5)[/tex]

[tex]y + 2 = x - 5[/tex]

[tex]y + 2 - 2 = x - 5 - 2[/tex]

[tex]y = x-7[/tex]

Answer:  [tex]y = x-7[/tex]

Answer:

1/4

Step-by-step explanation:

y=X equation is a direct variation function.

Answer:

Can we have a picture please? That would help a lot! Thanks!~

Step-by-step explanation:

Answer:

Slope m = -5

y intercept = 4

so the equation of the line is,

y = -5x+4

Plot two points, (0,4) and (1,-1)

then connect them, I've attached a graph, your graph should look like that

Answered by GAUTHMATH

Answer:

y=-5x+4

Step-by-step explanation:

y=mx+b

the slope is m

the y intercept is b

-5/1= one right and down 5

4 is the starting point on the y-axis (the vertical one)

Answer:

C

Step-by-step explanation:

Answer:

Generally, the higher the temperature, the larger the population.

Step-by-step explanation:

The line goes from left to right, and from down to up, so we can see that the temperature affects the population at the pool.

Answer:

19.5

Step-by-step explanation:

Answer:

k = 2

Step-by-step explanation:

f(x) and g(x) = f(x) + k

G(x) is the function f(x) moved up k units

G(x) is moved up 2 units so k is 2

Answer:

The answer is k = 2. The value of k is 2.

Step-by-step explanation:

I hope this answers your question :) Have a great day :)